Question

Form a quadratic polynomial of which one zero is 6-√5 and sum of the zeroes is 12.

Answer 1

`x^2-12x+31=0`

Explanation:

Say m and n are the zeroes of the polynomial, m is the known zero

First, we have to find n.

`6-\sqrt5 + n = 12\\n = 12 - 6 + \sqrt5\\n = 6+\sqrt5`

Then, we can use the known zeroes to form the quadratic equation
`(x-(6-\sqrt5))(x-(6+\sqrt5)=0\\x^2-6x-\sqrt5x-6x+\sqrt5x+36-5=0\\x^2-12x+31=0`